Can I help you?

I might be sensitive to others needs (common sense is a good guide here), I might be good at seeing how someone feels (faces don't lie), but sometimes I don't have a clue what some people want. I blame myself because I get so caught up in my own head, but I also wonder why a lot of the people I surround myself with seem to have such a hard time articulating what it is they want. Embarrassment? Fear? Guilt? Shame? for having whatever feeling it is they have or thing they want? Sometimes I feel like it comes to the point of them feeling I let them walk all over them before they finally speak up.
Then, once they are at the breaking point, they just take things out of context and twist them into something they aren't to justify how they have been feeling over the period in question. Recently I've tried to do a better job of expressing gratitude along the way but even that doesn't even seem to help. Even directly saying "hey, is something wrong? is there anything I can do?" won't elicit the direction I need. The basic response is always "Oh I'm fine. Don't worry about it." Even then, if I keep trying and tell them I really mean it and want to help, most of the time it won't draw out an explanation. I'll need to try/read/ask/think about this one some more, but I wish the people in my life I care about would make it easier for me to help them...